1. Field of The Invention
The present invention relates to a method for measuring the frequency of a sinusoidal signal.
2. Description of The Related Art
A conventional frequency measuring system, for instance the demodulator in an FM radio, is based on changing the sinusoidal signal into a digital pulse train and then calculating the frequency by counting the number of pulses during a certain period of time. Also when controlling Voltage Controlled Oscillators, VCO, by means of Phase Locked Loops, PLL, the output signal is converted to a pulse train which is digitally divided and phase compared with a digital reference frequency, usually from a frequency stable crystal oscillator.
A common feature of these two methods is that the signal which is the subject of the frequency measurement is limited in terms of amplitude to give a binary signal, and is divided in respect of frequency. In these processes, valuable information disappears that could be used to determine the frequency with increased speed and/or accuracy.
The signal V(t), see FIG. 1, is defined in the following as V(t)=A sin(xcfx89t+xcex1), where the amplitude is A, the angular frequency xcfx89=2xcfx80f and f is the frequency to be determined. Assuming that A is essentially constant during the time of the frequency measurement, it is easy to derive that
V(t)+V(txe2x88x922h)=A(sin(xcfx89(txe2x88x92h)+xcex1+xcfx89h)+sin(xcfx89(t xe2x88x92h)+xcex1xe2x88x92xcfx89h))=2Asin(xcfx89(txe2x88x92h)+xcex1)cos(xcfx89h)=2V(txe2x88x92h)cos(xcfx89h)
or vice versa                                                         V              ⁡                              (                t                )                                      +                          V              ⁡                              (                                  t                  -                                      2                    ⁢                    h                                                  )                                              2                =                  cos          ⁢                      xe2x80x83                    ⁢                      (                          ω              ⁢                              xe2x80x83                            ⁢              h                        )                    ⁢                      xe2x80x83                    ⁢                      V            ⁡                          (                              t                -                h                            )                                                          (                  equation          ⁢                      xe2x80x83                    ⁢          1                )            
This is a classical relation which is to be found in several sources, for instance in the journal xe2x80x9cFrequenzxe2x80x9d, Vol. 27, No. 11, 1973, Berlin, pp 309-311: xe2x80x9cFrequenzbestimmung durch Signalabtastungxe2x80x9d, and means that the frequency can essentially be calculated directly from                                           cos            ⁢                          xe2x80x83                        ⁢                          (                              ω                ⁢                                  xe2x80x83                                ⁢                h                            )                                =                                                                                          V                    ⁡                                          (                      t                      )                                                        +                                      V                    ⁡                                          (                                              t                        -                                                  2                          ⁢                          h                                                                    )                                                                      2                            ⟹                              
                            ⁢                              f                ⁡                                  (                  t                  )                                                      =                                          1                                  2                  ⁢                                      xe2x80x83                                    ⁢                  π                  ⁢                                      xe2x80x83                                    ⁢                  h                                            ⁢                              (                                                      2                    ⁢                                          xe2x80x83                                        ⁢                    π                    ⁢                                          xe2x80x83                                        ⁢                    n                                    ±                                      arccos                    ⁢                                          xe2x80x83                                        ⁢                                          (                                                                                                    V                            ⁡                                                          (                              t                              )                                                                                +                                                      V                            ⁡                                                          (                                                              t                                -                                                                  2                                  ⁢                                  h                                                                                            )                                                                                                                                2                          ⁢                                                      V                            ⁡                                                          (                                                              t                                -                                                                  2                                  ⁢                                  h                                                                                            )                                                                                                                          )                                                                      )                                                    ,                  xe2x80x83                ⁢                  n          ∈          Z                                    (                  equation          ⁢                      xe2x80x83                    ⁢          2                )            
where Z is the set of all integers; oh designates the normalised frequency.
The ambiguity in the arccos function is avoided (n=0) if the measurement frequency fs=1/h is at least twice as fast as the highest frequency that is measured. The higher frequencies are therefore usually filtered away in an analog way before the measurements are taken with a so-called anti-aliasing filter. The drawback of this filtering, however, is that higher frequencies then cannot be measured. In the invention defined in this patent application, an anti-aliasing filter is normally not used.
Directly utilising the algorithm according to (equation 2) for frequency determination causes numerical problems in the cases where V(txe2x88x92h)≈0. Moreover, only three measured values are used for the frequency determination, which gives the advantage that the method will be fast, but also the drawback that noise, quantization errors etc, if present, result in corresponding errors in the frequency estimation.
The present invention solves these two problems with the aid of a recursive frequency estimation in the fashion that is evident from the following independent claim. The remaining claims concern advantageous embodiments of the invention.
The invention will now be described in more detail with reference to the accompanying drawings, in which
FIG. 1 shows a description of a sinusoidal signal observed at a time interval of h seconds,
FIG. 2 is a block diagram of a frequency measurement device which in one step, (equation 3.1) and (equation 3.2), uses the invention,
FIG. 3 is a block diagram of a frequency measurement device which in two steps, (equation 3.1) and (equation 3.2), and, respectively, (equation 4.1) and (equation 4.2), uses the invention,
FIG. 4 illustrates a digital implementation of a frequency measurement device in one step according to the invention, and
FIG. 5 shows an analog implementation of a frequency measurement device in one step according to the invention.